Question

A boy walks 10 km due east, then takes a turn of 60° north of east and walks another 20 km to reach school. One day he finds a shortcut that takes him directly to school along a straight line path. Find the distance that he has to travel now, and the direction of the shortcut.​

Answer 1

Answer:

in order to find the distance we need to find the resultant of the two distance vectors given and also find its direction so,

R=√A^2+B^2+2ABcos©

R=√10^2+20^2+2×10×20×cos60

R=√100+400+400×1/2

R=√100+400+200

R=√600

R=10√6 km

to find direction

tan®=Bsin©/A+Bcos©

tan®=20×√3/2÷10+20×1/2

tan®=10√3/10+10

tan®=10√3/20

tan®=√3/2

®=tan^-1(√3/2)

therefore he now has to travel 10√6 km in a direction making an angle of tan^-1(√3/2) with the A distance vector.